Study of Graphene Networks and Line Graph of Graphene Networks via NM-Polynomial and Topological Indices

Abstract

The topological invariants are related to the molecular graph of the chemical structure and are numerical numbers that help us to understand the topology of the concerned chemical structure. With the help of these numbers, many properties of graphene can be guessed without preforming any experiment. Huge amount of calculations are required to obtain topological invariants for graphene, but by applying basic calculus roles, neighborhood $M$ -polynomial of graphene gives its indices. The aim of this work is to compute neighborhood degree-dependent indices for the graph of graphene and the line graph of subdivision graph of graphene. Firstly, we establish neighborhood M-polynomial of these families of graphs, and then, by applying basic calculus, we obtain several neighborhood degree-dependent indices. Our results play an important role to understand graphene and enhance its abilities.